How do you find the center of an equilateral triangle?

Question

If you have an equilateral triangle with the point coordinates of (x1, y1), (x2, y2), and (x3, y3), I need to find the coordinates of the middle point of the triangle. None of the sides of the triangle are running parrallel with either the x axis or y axis.

I really hope someone can help me with this since I have been trying to do it for a couple of hours now :) Thanks in advance.

Just to mention, I'm looking to do this to add it to a program I'm making, so I really need some kinda of formula that will let me take the coordinates of the corner points and come out with the coordinates of the center point. :) Cheers.

Answer 1

The center of a triangle is 2/3 the distance from the midpoint of one edge to the the opposite vertex.

So do use pythagorus with c=y2-y1, b = 1/2 (y3-y1) to find a

a= sqrt([y2-y1]^2+[1/2 (y3-y1)]^2)

a will be the length from the midpoint to the opposite corner so you just take 2/3

So the centre will be

2/3 [sqrt([y2-y1]^2+[1/2 (y3-y1)]^2)] from vertex y1

Hope it helps.

Answer 2

1) find the midpoint of each line
2) draw a line from the midpoint to the point at the opposite end of the triangle.
3) the intersection of the 3 should be the center.

If you are looking to solve it with a formula, i am sorry but i dont know.

Answer 3

You can bisect the line from any of the two points, going through the third. Then do this again with any other two points and the third. Where these two bisectors meet will be the center of the triangle.

Answer 4

You could find the equations of the perpendicular bisectors of two of the sides (because you should be able to find their slopes), then solve their system of equations. The solution of the system will be the geometric center of the equilateral triangle.